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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2601.21575 |
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| _version_ | 1866917231439380480 |
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| author | Sahu, Kirti Mehatari, Ranjit |
| author_facet | Sahu, Kirti Mehatari, Ranjit |
| contents | A finite non-abelian group $H$ is hamiltonian if all of its subgroups are normal. We compute the minimal orders of graphs having a hamiltonian group as their automorphism group. The fixing number of a graph $Γ$ is the minimum cardinality of a subset $S$ of $V(Γ)$ such that the stabilizer of $S$ is trivial. For a given finite group $G$, the fixing set is defined as the set comprising all possible fixing numbers of graphs having group $G$ as their automorphism groups. We determine the fixing sets corresponding to finite hamiltonian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21575 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On minimal graphs for hamiltonian groups and their fixing set Sahu, Kirti Mehatari, Ranjit Combinatorics 05C25 A finite non-abelian group $H$ is hamiltonian if all of its subgroups are normal. We compute the minimal orders of graphs having a hamiltonian group as their automorphism group. The fixing number of a graph $Γ$ is the minimum cardinality of a subset $S$ of $V(Γ)$ such that the stabilizer of $S$ is trivial. For a given finite group $G$, the fixing set is defined as the set comprising all possible fixing numbers of graphs having group $G$ as their automorphism groups. We determine the fixing sets corresponding to finite hamiltonian groups. |
| title | On minimal graphs for hamiltonian groups and their fixing set |
| topic | Combinatorics 05C25 |
| url | https://arxiv.org/abs/2601.21575 |